A176853 Given a(n) as d digits in length, partition the binary representation of a(n) into d-digit numbers from left to right and add them as if they were decimal numbers.

1, 1, 2, 1, 2, 2, 3, 1, 2, 20, 21, 11, 12, 21, 22, 10, 11, 11, 12, 20, 21, 21, 22, 11, 12, 12, 13, 21, 22, 22, 23, 10, 11, 20, 21, 11, 12, 21, 22, 20, 21, 30, 31, 21, 22, 31, 32, 11, 12, 21, 22, 12, 13, 22, 23, 21, 22, 31, 32, 22, 23, 32, 33, 10, 11, 11, 12, 20, 21, 21, 22, 11

Offset

1,3

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

a(9) = 2 because binary(9) = "1001" and 1+0+0+1=2.
a(10)= 20 because binary(10) = "1010" and 10+10=20.
a(31)= 23 because binary(31) = "11111" and 11+11+1=23.
a(100)= 120 because binary(100)= "1100100" and 110+010+0=120.
Note that several a(n) are equivalent to n: [1,20,21,1212,1213,10310,10311].

Mathematica

f[n_]:=Module[{id=IntegerDigits[n, 2], len=IntegerLength[n]}, Total[ FromDigits/@ Partition[ IntegerDigits[ n, 2], len, len, {1, 1}, {}]]]; Array[f, 80] (* Harvey P. Dale, Jun 19 2018 *)

Crossrefs

Sequence in context: A333831 A202389 A210868 * A261787 A302480 A329656

Adjacent sequences: A176850 A176851 A176852 * A176854 A176855 A176856

Keyword

base,easy,nonn

Author

Gil Broussard, Apr 27 2010

Status

approved